10 Search Results for "Bhattacharya, Binay"

Document
DOI: 10.4230/LIPIcs.IPEC.2025.8
Binary k-Center with Missing Entries: Structure Leads to Tractability

Authors: Tobias Friedrich, Kirill Simonov, and Farehe Soheil

Published in: LIPIcs, Volume 358, 20th International Symposium on Parameterized and Exact Computation (IPEC 2025)

Abstract
k-Center clustering is a fundamental classification problem, where the task is to categorize the given collection of entities into k clusters and come up with a representative for each cluster, so that the maximum distance between an entity and its representative is minimized. In this work, we focus on the setting where the entities are represented by binary vectors with missing entries, which model incomplete categorical data. This version of the problem has wide applications, from predictive analytics to bioinformatics. Our main finding is that the problem, which is notoriously hard from the classical complexity viewpoint, becomes tractable as soon as the known entries are sparse and exhibit a certain structure. Formally, we show fixed-parameter tractable algorithms for the parameters vertex cover, fracture number, and treewidth of the row-column graph, which encodes the positions of the known entries of the matrix. Additionally, we tie the complexity of the 1-cluster variant of the problem, which is famous under the name Closest String, to the complexity of solving integer linear programs with few constraints. This implies, in particular, that improving upon the running times of our algorithms would lead to more efficient algorithms for integer linear programming in general.
Cite as

Tobias Friedrich, Kirill Simonov, and Farehe Soheil. Binary k-Center with Missing Entries: Structure Leads to Tractability. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 8:1-8:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{friedrich_et_al:LIPIcs.IPEC.2025.8,
  author =	{Friedrich, Tobias and Simonov, Kirill and Soheil, Farehe},
  title =	{{Binary k-Center with Missing Entries: Structure Leads to Tractability}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{8:1--8:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-407-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{358},
  editor =	{Agrawal, Akanksha and van Leeuwen, Erik Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.8},
  URN =		{urn:nbn:de:0030-drops-251403},
  doi =		{10.4230/LIPIcs.IPEC.2025.8},
  annote =	{Keywords: Clustering, Missing Entries, k-Center, Parameterized Algorithms}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.63
Connected k-Median with Disjoint and Non-Disjoint Clusters

Authors: Jan Eube, Kelin Luo, Dorian Reineccius, Heiko Röglin, and Melanie Schmidt

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
The connected k-median problem is a constrained clustering problem that combines distance-based k-clustering with connectivity information. The problem allows to input a metric space and an unweighted undirected connectivity graph that is completely unrelated to the metric space. The goal is to compute k centers and corresponding clusters such that each cluster forms a connected subgraph of G, and such that the k-median cost is minimized. The problem has applications in very different fields like geodesy (particularly districting), social network analysis (especially community detection), or bioinformatics. We study a version with overlapping clusters where points can be part of multiple clusters which is natural for the use case of community detection. This problem variant is Ω(log n)-hard to approximate, and our main result is an 𝒪(k² log n)-approximation algorithm for the problem. We complement it with an Ω(n^{1-ε})-hardness result for the case of disjoint clusters without overlap with general connectivity graphs, as well as an exact algorithm in this setting if the connectivity graph is a tree.
Cite as

Jan Eube, Kelin Luo, Dorian Reineccius, Heiko Röglin, and Melanie Schmidt. Connected k-Median with Disjoint and Non-Disjoint Clusters. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 63:1-63:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{eube_et_al:LIPIcs.ESA.2025.63,
  author =	{Eube, Jan and Luo, Kelin and Reineccius, Dorian and R\"{o}glin, Heiko and Schmidt, Melanie},
  title =	{{Connected k-Median with Disjoint and Non-Disjoint Clusters}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{63:1--63:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.63},
  URN =		{urn:nbn:de:0030-drops-245317},
  doi =		{10.4230/LIPIcs.ESA.2025.63},
  annote =	{Keywords: Clustering, Connectivity constraints, Approximation algorithms}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.39
Sweeping a Domain with Line-Of-Sight Between Covisible Agents

Authors: Kien C. Huynh, Joseph S. B. Mitchell, and Valentin Polishchuk

Published in: LIPIcs, Volume 349, 19th International Symposium on Algorithms and Data Structures (WADS 2025)

Abstract
We consider sweeping a polygonal domain using variable-length segments whose endpoints can be considered to be mobile agents moving with bounded speeds; a point in the domain is swept when it belongs to one of the segments. The objective is to sweep the domain as quickly as possible. We show that the problem is NP-hard even in simple polygons and even for a single segment (two agents), and give constant-factor approximation algorithms, both for simple polygons and polygons with holes. Our approximations are obtained by introducing a new type of "window partition" of the polygon, which may find other applications. For domains with holes, our results are based on a non-trivial topological argument proving a surprising fact: a connected subset of the domain, whose points are swept but not directly touched by the agents, may contain at most one hole.
Cite as

Kien C. Huynh, Joseph S. B. Mitchell, and Valentin Polishchuk. Sweeping a Domain with Line-Of-Sight Between Covisible Agents. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 39:1-39:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{huynh_et_al:LIPIcs.WADS.2025.39,
  author =	{Huynh, Kien C. and Mitchell, Joseph S. B. and Polishchuk, Valentin},
  title =	{{Sweeping a Domain with Line-Of-Sight Between Covisible Agents}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{39:1--39:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-398-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{349},
  editor =	{Morin, Pat and Oh, Eunjin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.39},
  URN =		{urn:nbn:de:0030-drops-242706},
  doi =		{10.4230/LIPIcs.WADS.2025.39},
  annote =	{Keywords: Polygon sweeping, collaborating agents, motion coordination, makespan optimization}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.25
Approximating Klee’s Measure Problem and a Lower Bound for Union Volume Estimation

Authors: Karl Bringmann, Kasper Green Larsen, André Nusser, Eva Rotenberg, and Yanheng Wang

Published in: LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025)

Abstract
Union volume estimation is a classical algorithmic problem. Given a family of objects O₁,…,O_n ⊂ ℝ^d, we want to approximate the volume of their union. In the special case where all objects are boxes (also called hyperrectangles) this is known as Klee’s measure problem. The state-of-the-art (1+ε)-approximation algorithm [Karp, Luby, Madras '89] for union volume estimation as well as Klee’s measure problem in constant dimension d uses a total of O(n/ε²) queries of three types: (i) determine the volume of O_i; (ii) sample a point uniformly at random from O_i; and (iii) ask whether a given point is contained in O_i. First, we show that if an algorithm learns about the objects only through these types of queries, then Ω(n/ε²) queries are necessary. In this sense, the complexity of [Karp, Luby, Madras '89] is optimal. Our lower bound holds even if the objects are equiponderous axis-aligned polygons in ℝ², if the containment query allows arbitrary (not necessarily sampled) points, and if the algorithm can spend arbitrary time and space examining the query responses. Second, we provide a more efficient approximation algorithm for Klee’s measure problem, which improves the running time from O(n/ε²) to O((n+1/ε²) ⋅ log^{O(d)} (n)). We circumvent our lower bound by exploiting the geometry of boxes in various ways: (1) We sort the boxes into classes of similar shapes after inspecting their corner coordinates. (2) With orthogonal range searching, we show how to sample points from the union of boxes in each class, and how to merge samples from different classes. (3) We bound the amount of wasted work by arguing that most pairs of classes have a small intersection.
Cite as

Karl Bringmann, Kasper Green Larsen, André Nusser, Eva Rotenberg, and Yanheng Wang. Approximating Klee’s Measure Problem and a Lower Bound for Union Volume Estimation. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 25:1-25:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bringmann_et_al:LIPIcs.SoCG.2025.25,
  author =	{Bringmann, Karl and Larsen, Kasper Green and Nusser, Andr\'{e} and Rotenberg, Eva and Wang, Yanheng},
  title =	{{Approximating Klee’s Measure Problem and a Lower Bound for Union Volume Estimation}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{25:1--25:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-370-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{332},
  editor =	{Aichholzer, Oswin and Wang, Haitao},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.25},
  URN =		{urn:nbn:de:0030-drops-231778},
  doi =		{10.4230/LIPIcs.SoCG.2025.25},
  annote =	{Keywords: approximation, volume of union, union of objects, query complexity}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.73
Dominating Set, Independent Set, Discrete k-Center, Dispersion, and Related Problems for Planar Points in Convex Position

Authors: Anastasiia Tkachenko and Haitao Wang

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
Given a set P of n points in the plane, its unit-disk graph G(P) is a graph with P as its vertex set such that two points of P are connected by an edge if their (Euclidean) distance is at most 1. We consider several classical problems on G(P) in a special setting when points of P are in convex position. These problems are all NP-hard in the general case. We present efficient algorithms for these problems under the convex position assumption. ● For the problem of finding the smallest dominating set of G(P), we present an O(knlog n) time algorithm, where k is the smallest dominating set size. We also consider the weighted case in which each point of P has a weight and the goal is to find a dominating set in G(P) with minimum total weight; our algorithm runs in O(n³log² n) time. In particular, for a given k, our algorithm can compute in O(kn²log² n) time a minimum weight dominating set of size at most k (if it exists). ● For the discrete k-center problem, which is to find a subset of k points in P (called centers) for a given k, such that the maximum distance between any point in P and its nearest center is minimized. We present an algorithm that solves the problem in O(min{n^{4/3}log n+knlog² n,k² nlog²n}) time, which is O(n²log² n) in the worst case when k = Θ(n). For comparison, the runtime of the current best algorithm for the continuous version of the problem where centers can be anywhere in the plane is O(n³ log n). ● For the problem of finding a maximum independent set in G(P), we give an algorithm of O(n^{7/2}) time and another randomized algorithm of O(n^{37/11}) expected time, which improve the previous best result of O(n⁶log n) time. Our algorithms can be extended to compute a maximum-weight independent set in G(P) with the same time complexities when points of P have weights. - If we are looking for an (unweighted) independent set of size 3, we derive an algorithm of O(nlog n) time; the previous best algorithm runs in O(n^{4/3}log² n) time (which works for the general case where points of P are not necessarily in convex position). - If points of P have weights and are not necessarily in convex position, we present an algorithm that can find a maximum-weight independent set of size 3 in O(n^{5/3+δ}) time for an arbitrarily small constant δ > 0. By slightly modifying the algorithm, a maximum-weight clique of size 3 can also be found within the same time complexity. ● For the dispersion problem, which is to find a subset of k points from P for a given k, such that the minimum pairwise distance of the points in the subset is maximized. We present an algorithm of O(n^{7/2}log n) time and another randomized algorithm of O(n^{37/11}log n) expected time, which improve the previous best result of O(n⁶) time. - If k = 3, we present an algorithm of O(nlog² n) time and another randomized algorithm of O(nlog n) expected time; the previous best algorithm runs in O(n^{4/3}log² n) time (which works for the general case where points of P are not necessarily in convex position).
Cite as

Anastasiia Tkachenko and Haitao Wang. Dominating Set, Independent Set, Discrete k-Center, Dispersion, and Related Problems for Planar Points in Convex Position. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 73:1-73:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{tkachenko_et_al:LIPIcs.STACS.2025.73,
  author =	{Tkachenko, Anastasiia and Wang, Haitao},
  title =	{{Dominating Set, Independent Set, Discrete k-Center, Dispersion, and Related Problems for Planar Points in Convex Position}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{73:1--73:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2025.73},
  URN =		{urn:nbn:de:0030-drops-228982},
  doi =		{10.4230/LIPIcs.STACS.2025.73},
  annote =	{Keywords: Dominating set, k-center, geometric set cover, independent set, clique, vertex cover, unit-disk graphs, convex position, dispersion, maximally separated sets}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2021.13
Locating Evacuation Centers Optimally in Path and Cycle Networks

Authors: Robert Benkoczi, Binay Bhattacharya, Yuya Higashikawa, Tsunehiko Kameda, Naoki Katoh, and Junichi Teruyama

Published in: OASIcs, Volume 96, 21st Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2021)

Abstract
We present dynamic flow algorithms to solve the k-sink problem whose aim is to locate k sinks (evacuation centers) in such a way that the evacuation time of the last evacuee is minimized. In the confluent model, the evacuees originating from or passing through a vertex must evacuate to the same sink, and most known results on the k-sink problem adopt the confluent model. When the edge capacities are uniform (resp. general), our algorithms for non-confluent flow in the path networks run in O(n + k² log² n) (resp. O(n log(n) + k² log⁵ n)) time, where n is the number of vertices. Our algorithms for cycle networks run in O(k²n log² n) (resp. O(k²n log⁵ n)) time, when the edge capacities are uniform (resp. general).
Cite as

Robert Benkoczi, Binay Bhattacharya, Yuya Higashikawa, Tsunehiko Kameda, Naoki Katoh, and Junichi Teruyama. Locating Evacuation Centers Optimally in Path and Cycle Networks. In 21st Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2021). Open Access Series in Informatics (OASIcs), Volume 96, pp. 13:1-13:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{benkoczi_et_al:OASIcs.ATMOS.2021.13,
  author =	{Benkoczi, Robert and Bhattacharya, Binay and Higashikawa, Yuya and Kameda, Tsunehiko and Katoh, Naoki and Teruyama, Junichi},
  title =	{{Locating Evacuation Centers Optimally in Path and Cycle Networks}},
  booktitle =	{21st Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2021)},
  pages =	{13:1--13:19},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-213-6},
  ISSN =	{2190-6807},
  year =	{2021},
  volume =	{96},
  editor =	{M\"{u}ller-Hannemann, Matthias and Perea, Federico},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2021.13},
  URN =		{urn:nbn:de:0030-drops-148825},
  doi =		{10.4230/OASIcs.ATMOS.2021.13},
  annote =	{Keywords: Efficient algorithms, facility location, minmax sink, evacuation problem, dynamic flow in network}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2019.27
The Weighted k-Center Problem in Trees for Fixed k

Authors: Binay Bhattacharya, Sandip Das, and Subhadeep Ranjan Dev

Published in: LIPIcs, Volume 149, 30th International Symposium on Algorithms and Computation (ISAAC 2019)

Abstract
We present a linear time algorithm for the weighted k-center problem on trees for fixed k. This partially settles the long-standing question about the lower bound on the time complexity of the problem. The current time complexity of the best-known algorithm for the problem with k as part of the input is O(n log n) by Wang et al. [Haitao Wang and Jingru Zhang, 2018]. Whether an O(n) time algorithm exists for arbitrary k is still open.
Cite as

Binay Bhattacharya, Sandip Das, and Subhadeep Ranjan Dev. The Weighted k-Center Problem in Trees for Fixed k. In 30th International Symposium on Algorithms and Computation (ISAAC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 149, pp. 27:1-27:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{bhattacharya_et_al:LIPIcs.ISAAC.2019.27,
  author =	{Bhattacharya, Binay and Das, Sandip and Dev, Subhadeep Ranjan},
  title =	{{The Weighted k-Center Problem in Trees for Fixed k}},
  booktitle =	{30th International Symposium on Algorithms and Computation (ISAAC 2019)},
  pages =	{27:1--27:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-130-6},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{149},
  editor =	{Lu, Pinyan and Zhang, Guochuan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2019.27},
  URN =		{urn:nbn:de:0030-drops-115238},
  doi =		{10.4230/LIPIcs.ISAAC.2019.27},
  annote =	{Keywords: facility location, prune and search, parametric search, k-center problem, conditional k-center problem, trees}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2018.14
An O(n^2 log^2 n) Time Algorithm for Minmax Regret Minsum Sink on Path Networks

Authors: Binay Bhattacharya, Yuya Higashikawa, Tsunehiko Kameda, and Naoki Katoh

Published in: LIPIcs, Volume 123, 29th International Symposium on Algorithms and Computation (ISAAC 2018)

Abstract
We model evacuation in emergency situations by dynamic flow in a network. We want to minimize the aggregate evacuation time to an evacuation center (called a sink) on a path network with uniform edge capacities. The evacuees are initially located at the vertices, but their precise numbers are unknown, and are given by upper and lower bounds. Under this assumption, we compute a sink location that minimizes the maximum "regret." We present the first sub-cubic time algorithm in n to solve this problem, where n is the number of vertices. Although we cast our problem as evacuation, our result is accurate if the "evacuees" are fluid-like continuous material, but is a good approximation for discrete evacuees.
Cite as

Binay Bhattacharya, Yuya Higashikawa, Tsunehiko Kameda, and Naoki Katoh. An O(n^2 log^2 n) Time Algorithm for Minmax Regret Minsum Sink on Path Networks. In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, pp. 14:1-14:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{bhattacharya_et_al:LIPIcs.ISAAC.2018.14,
  author =	{Bhattacharya, Binay and Higashikawa, Yuya and Kameda, Tsunehiko and Katoh, Naoki},
  title =	{{An O(n^2 log^2 n) Time Algorithm for Minmax Regret Minsum Sink on Path Networks}},
  booktitle =	{29th International Symposium on Algorithms and Computation (ISAAC 2018)},
  pages =	{14:1--14:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-094-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{123},
  editor =	{Hsu, Wen-Lian and Lee, Der-Tsai and Liao, Chung-Shou},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2018.14},
  URN =		{urn:nbn:de:0030-drops-99624},
  doi =		{10.4230/LIPIcs.ISAAC.2018.14},
  annote =	{Keywords: Facility location, minsum sink, evacuation problem, minmax regret, dynamic flow path network}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2016.6
The p-Center Problem in Tree Networks Revisited

Authors: Aritra Banik, Binay Bhattacharya, Sandip Das, Tsunehiko Kameda, and Zhao Song

Published in: LIPIcs, Volume 53, 15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016)

Abstract
We present two improved algorithms for weighted discrete p-center problem for tree networks with n vertices. One of our proposed algorithms runs in O(n*log(n) + p*log^2(n) * log(n/p)) time. For all values of p, our algorithm thus runs as fast as or faster than the most efficient O(n*log^2(n)) time algorithm obtained by applying Cole's [1987] speed-up technique to the algorithm due to Megiddo and Tamir [1983], which has remained unchallenged for nearly 30 years. Our other algorithm, which is more practical, runs in O(n*log(n) + p^2*log^2(n/p)) time, and when p=O(sqrt(n)) it is faster than Megiddo and Tamir's O(n*log^2(n) * log(log(n))) time algorithm [1983].
Cite as

Aritra Banik, Binay Bhattacharya, Sandip Das, Tsunehiko Kameda, and Zhao Song. The p-Center Problem in Tree Networks Revisited. In 15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 53, pp. 6:1-6:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{banik_et_al:LIPIcs.SWAT.2016.6,
  author =	{Banik, Aritra and Bhattacharya, Binay and Das, Sandip and Kameda, Tsunehiko and Song, Zhao},
  title =	{{The p-Center Problem in Tree Networks Revisited}},
  booktitle =	{15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016)},
  pages =	{6:1--6:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-011-8},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{53},
  editor =	{Pagh, Rasmus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2016.6},
  URN =		{urn:nbn:de:0030-drops-60296},
  doi =		{10.4230/LIPIcs.SWAT.2016.6},
  annote =	{Keywords: Facility location, p-center, parametric search, tree network, sorting network}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2012.325
k-delivery traveling salesman problem on tree networks

Authors: Binay Bhattacharya and Yuzhuang Hu

Published in: LIPIcs, Volume 18, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)

Abstract
In this paper we study the k-delivery traveling salesman problem (TSP)on trees, a variant of the non-preemptive capacitated vehicle routing problem with pickups and deliveries. We are given n pickup locations and n delivery locations on trees, with exactly one item at each pickup location. The k-delivery TSP is to find a minimum length tour by a vehicle of finite capacity k to pick up and deliver exactly one item to each delivery location. We show that an optimal solution for the k-delivery TSP on paths can be found that allows succinct representations of the routes. By exploring the symmetry inherent in the k-delivery TSP, we design a 5/3-approximation algorithm for the k-delivery TSP on trees of arbitrary heights. The ratio can be improved to (3/2 - 1/2k) for the problem on trees of height 2. The developed algorithms are based on the following observation: under certain conditions, it makes sense for a non-empty vehicle to turn around and pick up additional loads.
Cite as

Binay Bhattacharya and Yuzhuang Hu. k-delivery traveling salesman problem on tree networks. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012). Leibniz International Proceedings in Informatics (LIPIcs), Volume 18, pp. 325-336, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)

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@InProceedings{bhattacharya_et_al:LIPIcs.FSTTCS.2012.325,
  author =	{Bhattacharya, Binay and Hu, Yuzhuang},
  title =	{{k-delivery traveling salesman problem on tree networks}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)},
  pages =	{325--336},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-47-7},
  ISSN =	{1868-8969},
  year =	{2012},
  volume =	{18},
  editor =	{D'Souza, Deepak and Radhakrishnan, Jaikumar and Telikepalli, Kavitha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2012.325},
  URN =		{urn:nbn:de:0030-drops-38707},
  doi =		{10.4230/LIPIcs.FSTTCS.2012.325},
  annote =	{Keywords: k-delivery traveling salesman problem, approximation algorithms}
}
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